FIVE MARTIAN YEARS OF MSL GALE CRATER CLOUD OPACITY
MEASUREMENTS: DETERMINING A SCATTERING PHASE FUNCTION
FOR THE APHELION CLOUD BELT
C. W. Hayes1 (hayes954@yorku.ca), J. L. Kloos2, C. L. Campbell1, A. C. Innanen1, H. M. Sapers1, and J. E.
Moores1. 1Centre for Research in Earth and Space Sciences, York University, Toronto, ON, Canada; 2Department
of Astronomy, University of Maryland, College Park, MD, USA.
Introduction:
The Martian climate is dominated by the seasonal
effects of the planet’s high orbital eccentricity
(~0.0935), which takes it ~20% closer to the Sun at
perihelion than at aphelion. This difference results in
significant variations in solar insolation and thus atmospheric conditions over the course of the Martian
year. Two Martian seasons can thus be defined: the
dusty season, which occurs around perihelion (Ls =
135° - 360°) and is characterized by higher temperatures and increased atmospheric dust loading; and the
cloudy season, which occurs around aphelion (Ls = 0°
- 135°) and is characterized by the formation of the
Aphelion Cloud Belt (ACB), a water-ice cloud feature
that surrounds the planet at latitudes between 10°S
and 30°N (Wolff et al., 1999).
Although the thickness of the ACB peaks around
10°N, the equatorial latitude of the Mars Science Laboratory (MSL) Curiosity rover landing site (~4.6°S)
allows for observations of the southern edge of the
ACB to be conducted from the ground. With this in
mind, a cloud observation campaign has been ongoing
since sol 24 with the goal of examining diurnal, annual, and interannual variations in cloud opacities,
morphologies, and altitudes, as well as their scattering
phase function.
Previous work (Moores et al., 2015; Kloos et al.,
2016; Kloos et al., 2018) examined the first two Martian years of data and found a slight increase in opacities in the early morning compared to the late afternoon, as well as increased opacities overall during the
ACB season. Kloos et al. (2018) also found very little
interannual variability in the opacity of ACB clouds
between MY 32 and MY 33, which is consistent with
orbital observations of the interannual consistency of
the ACB (e.g. Tamppari et al., 2003; Liu et al., 2003;
Smith et al., 2004; Hale et al., 2011). Although an apparent increase in opacity in MY 33 is observed, it is
attributed to an increased number of early morning
observations, which pulled the average up on account
of their higher opacities compared to afternoon
clouds.
However, because consistent early morning observations were not conducted until MY 33, it was not
possible for Kloos et al. (2018) to determine if the diurnal difference in opacity was a persistent or transient feature of the ACB. With five MYs of data processed, three and a half of which include full diurnal
coverage, we can now fully assess the year-to-year
variability of ACB clouds over Gale Crater.

Methods:
Atmospheric movies. Using the Navigation Cameras (Navcams) onboard MSL, two types of atmospheric movies are acquired on a regular cadence: Zenith Movies (ZMs) and Suprahorizon Movies (SHMs).
ZMs are pointed almost directly straight up (~85°), allowing for the determination of the clouds’ angular
velocities and direction of motion; SHMs are pointed
more obliquely (~26°), permitting a more robust examination of cloud morphologies. Both movies consist of eight frames taken across ~6 minutes.
On average, ZMs are acquired at a reduced cadence compared to SHMs because MSL’s equatorial
location mandates a two and a half hour keepout time
from local noon to avoid pointing the Navcams directly at the Sun.

Figure 1. Temporal distribution of ZMs (red circles) and
SHMs (black triangles) over the length of the MSL mission.
The ZM keepout window is evident, as well as the addition
of dedicated observation time in the morning be-ginning in
MY33. The highlighted observations are CAO ZMs and
SPENDIs/Super-SPENDIs, illustrating how the addition of
these observations enhanced the cadence of opacity measurements. The gap in coverage around 10:00 LTST is the
result of the rover’s uplink schedule, which precludes observations.

In recent MYs, several new observations have
been introduced that have allowed for an increased cadence of both ZMs and SHMs. First is the Cloud Altitude Observation (CAO; Campbell et al. 2020),
which is executed ~once a week between 14:30–16:00
LTST during the ACB season. Though its primary
purpose is to measure cloud altitudes, it includes a ZM
that is identical to the standard cadence ZMs. The second new observation is a shunt prevention activity,
designed to partially drain the rover’s battery to prevent it from sitting fully-charged for an extended period of time. Two versions of this activity were designed, with low (SPENDI; Shunt Prevention ENV
Navcam Drop-In) or high (Super-SPENDI) data

volumes to meet the rover’s operational needs at different times of the year. Both versions consist of movies taken at six different pointings, two of which replicate the SHM parameters. They are not subject to the
typical science block time limitations, and so have allowed for the acquisition of SHMs at atypical times of
day, improving the diurnal coverage.
Opacity measurement. Martian clouds are typically very optically thin, so much so that they are
rarely visible in the raw movie frames. Consequently,
a technique known as mean-frame subtraction is used
to enhance the visibility of clouds in each movie. Each
pixel is averaged across all eight frames of the movie
to produce a mean frame, which is then subtracted
from each individual frame, leaving behind only the
time-varying portion of the image (i.e., the clouds).

Figure 3. An example radiance map of the time-variable
component of frame 5 of the sol 2633 ZM. The high and low
radiance points are indicated by the red and white markers,
respectively.

Figure 2. One frame from a SHM taken on sol 1924 before
(left) and after (right) mean-frame subtraction, showcasing
the ability of this method to extract the optically thin clouds
from the background.

Following mean-frame subtraction, high- and
low-radiance points, corresponding to a cloudy and
non-cloudy portion of the image, respectively, are
chosen from one frame through visual inspection. The
difference in radiance between these two points
(Il,VAR) is then used to determine the cloud opacity.
Opacities are calculated using two equations that
make different assumptions about the nature of the
clouds being observed, assumptions that are valid at
different points during the year. The first of these
equations, the high-cloud formula (Eq. 1), is used during the ACB season. It assumes that the clouds are at
high altitudes and primarily comprised of water ice
crystals. The second, the whole atmosphere formula
(Eq. 2), assumes that MSL is observing low-altitude
dust clouds. Opacities are found using both methods,
then one is selected as the preferred opacity depending on whether equatorial water ice clouds are observed by the Mars Color Imager onboard the Mars
Reconnaissance Orbiter at the time the movie was
taken. For full derivations of these equations, see
Kloos et al. (2016) and Moores et al. (2010).
Δτ!" =

4πµ𝐼#,%&' Δλ
τ
𝑃(Θ)𝐹#,( 𝑒𝑥𝑝 1− )*+
µ 3

ΔτWA = −𝑙𝑛 81 + 𝑎 −

𝑎
;
𝑒𝑥𝑝(−τ)*+ )

(1)

(2)

Working through these equations term by term, µ
is the cosine of the zenith angle (5° for ZMs, 64° for
SHMs), Il,VAR is the difference in radiance between
the selected high and low points, and Dl is the
Navcam bandpass (250 nm). P(Q) is the scattering
phase function of the clouds, Fl,0 is the in-band solar
flux at the top of the atmosphere, and tCOL is the atmospheric column density, determined through Mastcam imaging of the solar disc every 5-10 sols (Lemmon, 2014). Finally, a is the fractional radiance, or the
ratio of Il,VAR and the mean radiance of the frame (𝑎 =
I#,./0 /I#,12/3 ).
Most of these terms are fairly well-determined.
The two that introduce the most uncertainty into the
opacity measurements are tCOL and P(Q). Because
tCOL is not acquired simultaneously (or even always
on the same sol) as the cloud movies, it is necessary
to interpolate between sols where tCOL is measured.
Though a linear interpolation is generally a good fit
(Kloos et al., 2018), brief jumps in optical depth over
short timescales have been measured near perihelion
by the UV sensors on the Rover Environmental Monitoring Station. If such an increase occurred while a
cloud observation was underway, a linear interpolation would be inappropriate.
P(Q) is assumed to be independent of scattering
angle, at a value of 𝑃 = 1/15, or the ratio between the
radiance and extinction coefficients for isotropic single scattering, the dominant form of radiative transfer
given the low opacities of the clouds. This value is
also consistent with measured cloud phase functions
in the vicinity of 90°, where most of the cloud movies
taken during MY 31–33 were acquired. Complementary observations of the phase function of Martian
clouds from MSL that are currently ongoing (Cooper

Figure 4. ZM cloud opacities as a function of phase angle. Note that these angles are measured with respect to the center
of the Navcam frame, and not the points where the opacity was measured. These two angles can be ±30° from each other
due to the wide FOV of the Navcams (45°). The red line is a moving average calculated with a window width of 25.

et al., 2019; Innanen et al. 2021) may lead to improved
precision in this term in the future.
Results:
With all movies acquired through Ls = 160° of
MY 36 processed, the record of cloud opacity measurements over Gale Crater has been extended from
two Martian years to five. Notably, we now have ~3.5
MY of full AM/PM coverage, allowing us to examine
interannual variability in diurnal opacity patterns for
the first time.
Observations at low phase angles. During our preliminary analysis of movies acquired during MY 34–
36, we discovered that the ZM and SHM datasets
were producing different results for the preferred
mean opacity during the ACB season. In theory, there
is no good reason why the clouds observed in a SHM
would be any different than those observed in a ZM,
particularly in those cases where the two movies are
taken < 10 minutes apart.
By comparing our results to those presented by
Kloos et al. (2018) for MY 31–33, it became clear that
the problem was arising from the ZM dataset. The
mean preferred ACB opacities as measured using the
SHMs showed very little interannual variability during the full five MYs of the mission, consistent with
expectations. However, the ZM opacities for MY 34–
36 are both higher and more variable than those for
MY 31–33.
Upon closer inspection, we realized that the mean
preferred opacities in the MY 34–36 ZM dataset are
being biased upward by a small number of extreme
outliers that were not present in the MY 31–33 observations. Almost all of these outliers were associated
with ZMs taken close to local noon, just outside of the
required keepout window. This suggests that at least
one of the high-cloud model’s assumptions is breaking down at low phase angles. Indeed, if we plot ZM
opacities as a function of the angle between the
Navcam pointing and the solar position vector (Figure
4), we can see that there is a clear upward trend towards low angles.
The most obvious candidate for the broken

assumption is the phase function term, P(Q). Kloos et
al. (2016) and Kloos et al. (2018) justified the choice
of a flat phase function as being consistent with optically thin terrestrial cirrus clouds for scattering angles
near 90°. As the Sun approaches the Navcam FOV,
we are observing the clouds at progressively smaller
scattering angles. Previously derived phase functions
for Martian water ice clouds using Viking (Clancy
and Lee, 1991), MGS (Clancy et al. 2003), and MSL
(Cooper et al., 2019; Innanen et al. 2021) data as well
as models of the phase function of different water ice
crystal geometries (Yang and Liou, 1996; Yang et al.
2010) all show significant upward deviations from our
flat assumption at scattering angles < 40–70°, consistent with the observed effect in our data.
Before our results can yield useful conclusions,
we must account for the deviation from our assumptions. The simplest way to do so would be to restrict
the dataset to only those where the phase function is
flat, throwing out potentially a third to half of the ZM
measurements, depending on where we make the cut.
Losing such a substantial number of observations
would be less than ideal, so it would be preferable to
find a way to correct our results, allowing for the use
of the entire dataset.
In principle, it would be possible for this correction to be performed using a previously derived phase
function for Martian water-ice clouds. However, we
are presented with an opportunity to derive our own
phase function. Because of the low interannual variability of the ACB, we can assume a constant “true”
value for its opacity (after considering seasonal and
diurnal effects) and determine what value of the phase
function is necessary to bring the calculated opacity
down to that value.
In addition to providing another point of comparison, the phase function that we will derive is also fundamentally different methodologically from those reported by Cooper et al. (2019) and Innanen et al.
(2021). Because the cloud opacity appears in their
phase function equation (a rearranged version of the
high-cloud formula), they must use time-averaged
water ice column opacities taken by the Mars Climate

Sounder in the vicinity of Gale Crater, which are not
necessarily representative of local conditions.
Effects of the MY 34 GDS. Our updated coverage
includes the global dust storm (GDS) that occurred in
MY 34 between Ls = 188° – 250° (Guzewich et al.,
2019). Previous works have found that the ACB in the
MY immediately following a GDS can be significantly more variable than those not preceded by a
GDS (Mateshvili et al. 2019; Wolff et al. 2019). Although the extremely high atmospheric opacity prevented cloud observations during the storm itself, it is
now possible to see if ground-based observations of
the ACB following the MY 34 GDS are consistent
with these prior observations.
If the MY 34 GDS did impact the opacity of the
MY 35 ACB, then that could be problematic for our
phase function calculation, as it assumes low interannual variability. However, we do not anticipate this to
be a serious problem. It is our expectation that such
an effect would expose itself both through the opacities measured at high scattering angles where the assumption of a flat phase function holds as well as
through changes in the shape of the derived phase
function at low scattering angles, as the phase function itself appears to be unaffected by GDS events (Innanen et al., 2021).
Summary:
The record of cloud opacities over Gale Crater as
measured by MSL has been extended from two Martian years to five, covering nearly the entire length of
the mission to date (sols 0–3360). We are now able to
fully assess interannual variability in diurnal opacity
patterns, as well as the effects of the MY 34 GDS on
the ACB. In doing so, we found a dependence of the
calculated opacities on the scattering angle that is inconsistent with our prior assumption of a flat phase
function. In correcting for this dependence, we have
an opportunity to derive a phase function for Martian
water-ice clouds that is independent of other data sets.
As of writing, the work to derive the phase function and correct the opacity measurements is ongoing.
By the time of the conference, we anticipate that we
will have a fully corrected record of cloud opacities
over Gale Crater through the MY 36 ACB season.
Acknowledgements:
Funding for this research was provided by the Canadian Space Agency MSL Participating Scientist
Program based on a NASA MSL PSP selection.
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